Nonlinear constrained vector optimization using Optimization Toolbox

I am attempting to reproduce a nonlinear constrained vector optimization result obtained in Heuett/Qian (2006) using the fmincon solver's SQP algorithm in the Optimization Toolbox.

The general optimization problem is given by

and the specific objective function of interest in this case is given by

where J, J+ , J-, Jext, and delta_mu are all vectors, Jext_D is an element of vector Jext, and S and K^T are matrices supplied by the nature of the system in question.

I have coded the objective function in heuett_simple.m:

function f = heuett_simple(J_ext, delta_mu)
f = J_ext(4) + dot(delta_mu)/2;
end

since Jext_D will be the fourth element of the vector J_ext

and the constraints in heuett_constraints.m:

function [c, ceq] = heuett_constraints(J, J_plus, J_minus, J_ext, delta_mu)
model = sbmlimport('heuett_simple.xml');
S = getstoichmatrix(model);
S = full(S);
K = [-0.7163, -0.3345;
     -0.3205, -0.4347;
     0.4710, -0.6349;
     -0.3958, 0.1001;
     -0.0752, 0.5348];

c = [];
ceq(1) = S*J + J_ext;
ceq(2) = transpose(K)*delta_mu;
ceq(3) = diag(exp(delta_mu))*J_plus - J_minus;
ceq(4) = J - J_plus + J_minus;
end

The specifications of model, S, and K are specific to the problem I am working on. S is a 4x5 matrix of type double. When I execute this problem using the Toolbox with the following setup (without bounds for the time being)

I receive the error

Index exceeds matrix dimensions.

Any idea what is causing my problem?

[Ingrid Tigges]

Would it be possible for you to provide a reproduction example? This helps answering this kind of questions a lot.

[Sam]

Sorry, what do you mean by a reproduction example?

Answer 1

[Sean de Wolski]

>>dbstop if error

Then run the code. This will stop on the line throwing the error and you can look at the index v. the size of your matrix and see what's happening.

[Sam]

Okay, I'm receiving the following error:

Index exceeds matrix dimensions.

Error in heuett_simple (line 2)
f = J_ext(4) + dot(delta_mu)/2;
Error in fmincon (line 635)
      initVals.f = feval(funfcn{3},X,varargin{:});

Caused by:
    Failure in initial user-supplied objective function evaluation. FMINCON cannot continue.

I suppose that this is because I am supplying an element of a vector in the objective function -- J_ext(4). Any advice for optimization with vectors?

[Adam Cutbill]

Can't you specific advice without recreating your inputs. My advice would be to put a breakpoint in your objfun and confun and make sure all the inputs are as you expect. Go from there.

[Matt J]

I suppose that this is because I am supplying an element of a vector in the objective function -- J_ext(4).

@Sam,

You still haven't followed Sean's advice about using dbstop. Had you done so, there would be nothing to "suppose". The program would pause at line 2 in heuett_simple() and you could show us directly what J_ext contains.

[Sam]

Hi Matt,

I did use dbstop, and as I result I realized that there was a problem with my supplied objective function (there is no J_ext in the workspace after running the code), so I'll try your suggestion below to feed the unknowns as a single variable.

Answer 2

[Matt J]

One of the errors you have is that you are feeding the unknowns to the objective function and constraints in multiple input arguments, e.g.,

 function f = heuett_simple(J_ext, delta_mu)
   f = J_ext(4) + dot(delta_mu)/2;
 end

All the unknowns must be fed in as a a single variable, like in the following

   function f = heuett_simple(unknowns)

      J_ext=unknowns(1:N);
      delta_mu=unknowns(N+1:end);

      f = J_ext(4) + dot(delta_mu)/2;
   end

and similarly with your constraints.

[Matt J]

Another error is that you have selected an initial point [0,0] consisting of only 2 elements, when you apparently have considerably more than 2 unknowns.